Toss the pork shoulder chunks with the cumin, oregano, and salt in a large Dutch oven or slow cooker.
Add the onion, garlic, bay leaves, orange juice and spent halves, lime juice, and water.
Cover and cook at a low simmer on the stovetop (or in a 300°F/150°C oven, or a slow cooker on low) for 3-3½ hours, until the pork shreds easily with a fork.
Meanwhile, combine the sliced red onion, lime juice, salt, and sugar in a jar. Let sit at room temperature for at least 20 minutes, tossing occasionally.
Remove the pork, discard the bay leaves and orange halves, and shred the meat with two forks. Spread the shredded pork on a sheet pan and broil for 5-7 minutes, or crisp in batches in a hot skillet, until the edges are browned and crispy.
Pile the crispy carnitas into warm corn tortillas and top with pickled red onion and chopped cilantro.
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